Hybrid Quantum-classical Approach Research Articles

Adaptive Circuit Learning of Born Machine: Towards Realization of Amplitude Embedding and Quantum Data Loading

Abstract Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups often predicated on access to an efficient data-loading oracle. In practice, constructing a circuit to prepare a generic $n$-qubit quantum state typically demands computational efforts scaling as $\mathcal{O}(2^n)$, posing a significant challenge for quantum algorithms to outperform their classical counterparts. To address this critical issue, various hybrid quantum-classical approaches have been proposed. However, many of these solutions favor simplistic circuit architectures, which are susceptible to substantial optimization challenges.

In this study, we harness quantum circuits as Born machines to generate probability distributions. Drawing inspiration from methods used to investigate electronic structures in quantum chemistry and condensed matter physics, we propose a framework called Adaptive Circuit Learning of Born Machine, which dynamically expands the ansatz circuit. Our algorithm is designed to selectively integrate two-qubit entangled gates that best capture the intricate entanglement present within the target state. 
Empirical experiments underscore the efficacy of our approach in encoding real-world data through amplitude embedding, demonstrating not only compliance with but also enhancement over the performance benchmarks set by prior research.

Accelerating quantum imaginary-time evolution with random measurements

Quantum imaginary-time evolution (QITE) is a promising tool to prepare thermal or ground states of Hamiltonians, as convergence is guaranteed when the evolved state overlaps with the ground state. However, its implementation using a a hybrid quantum-classical approach, where the dynamics of the parameters of the quantum circuit are derived by McLachlan's variational principle, is impractical as the number of parameters m increases, since each step in the evolution takes Θ(m2) state preparations to calculate the quantum Fisher information matrix (QFIM). In this work, we accelerate QITE by rapid estimation of the QFIM, while conserving the convergence guarantees to the extent possible. To this end, we prove that if a parameterized state is rotated by a 2-design and measured in the computational basis, then the QFIM can be inferred from partial derivative cross correlations of the probability outcomes. One sample estimate costs only Θ(m) state preparations, leading to rapid QFIM estimation when a few samples suffice. The second family of estimators takes greater liberties and replace QFIMs with averaged classical Fisher information matrices (CFIMs). In an extreme special case optimized for rapid (over accurate) descent, just one CFIM sample is drawn. We justify the second estimator family by proving rapid descent. Guided by these results, we propose the algorithm, which we showcase and test in several molecular systems, with the goal of preparing ground states. Published by the American Physical Society 2025

SHARC meets TEQUILA: mixed quantum-classical dynamics on a quantum computer using a hybrid quantum-classical algorithm.

Recent developments in quantum computing are highly promising, particularly in the realm of quantum chemistry. Due to the noisy nature of currently available quantum hardware, hybrid quantum-classical algorithms have emerged as a reliable option for near-term simulations. Mixed quantum-classical dynamics methods effectively capture nonadiabatic effects by integrating classical nuclear dynamics with quantum chemical computations of the electronic properties. However, these methods face challenges due to the high computational cost of the quantum chemistry part. To mitigate the computational demand, we propose a method where the required electronic properties are computed through a hybrid quantum-classical approach that combines classical and quantum hardware. This framework employs the variational quantum eigensolver and variational quantum deflation algorithms to obtain ground and excited state energies, gradients, nonadiabatic coupling vectors, and transition dipole moments. These quantities are used to propagate the nonadiabatic molecular dynamics using the Tully's fewest switches surface hopping method, although the implementation is also compatible with other molecular dynamics approaches. The approach, implemented by integrating the molecular dynamics program package SHARC with the TEQUILA quantum computing framework, is validated by studying the cis-trans photoisomerization of methanimine and the electronic relaxation of ethylene. The results show qualitatively accurate molecular dynamics that align with experimental findings and other computational studies. This work is expected to mark a significant step towards achieving a "quantum advantage" for realistic chemical simulations.

Mechanism of ultrafast flavin photoreduction in the active site of flavoenzyme LSD1 histone demethylase.

Photoreduction of oxidized flavins has a functional role in photocatalytic and photoreceptor flavoproteins. In flavoproteins without light-dependent physiological functions, ultrafast, reversible flavin photoreduction is supposedly photoprotective by nature, and holds potential for nonnatural photocatalytic applications. In this work, we combine protein mutagenesis, ultrafast spectroscopy, molecular dynamics simulations and quantum mechanics calculations to investigate the nonfunctional flavin photoreduction in a flavoenzyme, lysine-specific demethylase 1 (LSD1) which is pivotal in DNA transcription. LSD1 harbors an oxidized flavin adenine dinucleotide (FAD) cofactor and multiple electron-donating residues in the active site. Upon photoexcitation, the FAD cofactor is photoreduced in <200 fs by electron transfer (ET) from nearby residue(s), and the charge pairs recombine in ca. 2 ps. Site-directed mutagenesis pinpoints a specific tryptophan residue, W751, as the primary electron donor, whereas a tyrosine residue, Y761, despite being located closer to the flavin ring, does not effectively contribute to the process. Based on a hybrid quantum-classical computational approach, we characterize the W751-FAD and Y761-FAD charge-transfer states (CTW751 and CTY761, respectively), as well as the FAD locally excited state (LEFAD), and demonstrate that the coupling between LEFAD and CTW751 is larger than those involving CTY761 by an order of magnitude, rationalizing the experimental observations. More generally, this work highlights the role of the intrinsic protein environment and details of donor-acceptor molecular configurations on the dynamics of short-range ET involving a flavin cofactor and amino acid residue(s).

Designing microplastic-binding peptides with a variational quantum circuit-based hybrid quantum-classical approach.

De novo peptide design exhibits great potential in materials engineering, particularly for the use of plastic-binding peptides to help remediate microplastic pollution. There are no known peptide binders for many plastics-a gap that can be filled with de novo design. Current computational methods for peptide design exhibit limitations in sampling and scaling that could be addressed with quantum computing. Hybrid quantum-classical methods can leverage complementary strengths of near-term quantum algorithms and classical techniques for complex tasks like peptide design. This work introduces a hybrid quantum-classical generative framework for designing plastic-binding peptides combining variational quantum circuits with a variational autoencoder network. We demonstrate the framework's effectiveness in generating peptide candidates, evaluate its efficiency for property-oriented design, and validate the candidates with molecular dynamics simulations. This quantum computing-based approach could accelerate the development of biomolecular tools for environmental and biomedical applications while advancing the study of biomolecular systems through quantum technologies.

Quantum Convolutional Neural Network: A Hybrid Quantum-Classical Approach for Iris Dataset Classification

This paper presents a hybrid quantum-classical machine learning model for classification tasks, integrating a 4-qubit quantum circuit with a classical neural network. The quantum circuit is designed to encode the features of the Iris dataset using angle embedding and entangling gates, thereby capturing complex feature relationships that are difficult for classical models alone. The model, which we term a Quantum Convolutional Neural Network (QCNN), was trained over 20 epochs, achievinga perfect 100% accuracy on the Iris dataset test set on 16 epoch. Our results demonstrate the potential of quantum-enhanced models in supervised learning tasks, particularly in efficiently encoding and processing data using quantum resources. We detail the quantum circuit design, parameterizedgate selection, and the integration of the quantum layer with classical neural network components.This work contributes to the growing body of research on hybrid quantum-classical models and theirapplicability to real-world datasets.

Unleashed from constrained optimization: quantum computing for quantum chemistry employing generator coordinate inspired method

Hybrid quantum-classical approaches offer potential solutions to quantum chemistry problems, yet they often manifest as constrained optimization problems. Here, we explore the interconnection between constrained optimization and generalized eigenvalue problems through the Unitary Coupled Cluster (UCC) excitation generators. Inspired by the generator coordinate method, we employ these UCC excitation generators to construct non-orthogonal, overcomplete many-body bases, projecting the system Hamiltonian into an effective Hamiltonian, which bypasses issues such as barren plateaus that heuristic numerical minimizers often encountered in standard variational quantum eigensolver (VQE). Diverging from conventional quantum subspace expansion methods, we introduce an adaptive scheme that robustly constructs the many-body basis sets from a pool of the UCC excitation generators. This scheme supports the development of a hierarchical ADAPT quantum-classical strategy, enabling a balanced interplay between subspace expansion and ansatz optimization to address complex, strongly correlated quantum chemical systems cost-effectively, setting the stage for more advanced quantum simulations in chemistry.

A Hybrid Quantum-Classical Model for Stock Price Prediction Using Quantum-Enhanced Long Short-Term Memory.

The stock markets have become a popular topic within machine learning (ML) communities, with one particular application being stock price prediction. However, accurately predicting the stock market is a challenging task due to the various factors within financial markets. With the introduction of ML, prediction techniques have become more efficient but computationally demanding for classical computers. Given the rise of quantum computing (QC), which holds great promise for being exponentially faster than current classical computers, it is natural to explore ML within the QC domain. In this study, we leverage a hybrid quantum-classical ML approach to predict a company's stock price. We integrate classical long short-term memory (LSTM) with QC, resulting in a new variant called QLSTM. We initially validate the proposed QLSTM model by leveraging an IBM quantum simulator running on a classical computer, after which we conduct predictions using an IBM real quantum computer. Thereafter, we evaluate the performance of our model using the root mean square error (RMSE) and prediction accuracy. Additionally, we perform a comparative analysis, evaluating the prediction performance of the QLSTM model against several other classical models. Further, we explore the impacts of hyperparameters on the QLSTM model to determine the best configuration. Our experimental results demonstrate that while the classical LSTM model achieved an RMSE of 0.0693 and a prediction accuracy of 0.8815, the QLSTM model exhibited superior performance, achieving values of 0.0602 and 0.9736, respectively. Furthermore, the QLSTM outperformed other classical models in both metrics.

Revolutionizing Optimization: The Game-Changing Power of Quantum Algorithms and Next-Generation Computational Technologies

Quantum algorithms offer promising advancements in solving complex optimization problems that are critical in various fields, including logistics, finance, and machine learning. Classical optimization techniques, while effective, often struggle with large-scale and high-dimensional data sets, leading to inefficiencies and long processing times.Quantum algorithms, leveraging the principles of superposition, entanglement, and quantum parallelism, provide a potential solution by exponentially speeding up certain computational tasks. This paper explores key quantum algorithms for optimization, including Grover's algorithm, the Quantum Approximate Optimization Algorithm (QAOA), and the Quantum Annealing method. We analyze their theoretical foundations, implementation challenges, and practical applications. Special attention is given to the performance comparisons between quantum and classical approaches in solving combinatorial optimization problems, such as the traveling salesman problem and portfolio optimization. We also discuss the limitations of current quantum hardware and the prospects for future improvements that could make quantum optimization algorithms more practical for real-world use.Our findings suggest that, while quantum algorithms are still in their early stages, they hold immense potential for transforming optimization in a variety of domains, offering new pathways toward more efficient problem-solving in both theoretical and applied contexts. we explore how hybrid quantum-classical approaches can enhance optimization results by combining the strengths of both paradigms. Future research directions are highlighted, focusing on improving quantum error correction, scaling quantum systems, and developing more robust quantum algorithms to tackle increasingly complex optimization problems.

Self-Consistent Determination of Single-Impurity Anderson Model Using Hybrid Quantum-Classical Approach on a Spin Quantum Simulator.

The accurate determination of the electronic structure of strongly correlated materials using first principle methods is of paramount importance in condensed matter physics, computational chemistry, and material science. However, due to the exponential scaling of computational resources, incorporating such materials into classical computation frameworks becomes prohibitively expensive. In 2016, Bauer etal. proposed a hybrid quantum-classical approach to correlated materials [B. Bauer et al., Hybrid quantum-classical approach to correlated materials, Phys. Rev. X 6, 031045 (2016).PRXHAE2160-330810.1103/PhysRevX.6.031045] that can efficiently tackle the electronic structure of complex correlated materials. Here, we experimentally demonstrate that approach to tackle the computational challenges associated with strongly correlated materials. By seamlessly integrating quantum computation into classical computers, we address the most computationally demanding aspect of the calculation, namely the computation of the Green's function, using a spin quantum processor. Furthermore, we realize a self-consistent determination of the single impurity Anderson model through a feedback loop between quantum and classical computations. A quantum phase transition in the Hubbard model from the metallic phase to the Mott insulator is observed as the strength of electron correlation increases. As the number of qubits with high control fidelity continues to grow, our experimental findings pave the way for solving even more complex models, such as strongly correlated crystalline materials or intricate molecules.

Simulation of open quantum systems via low-depth convex unitary evolutions

Simulating physical systems on quantum devices is one of the most promising applications of quantum technology. Current quantum approaches to simulating open quantum systems are still practically challenging on NISQ-era devices, because they typically require ancilla qubits and extensive controlled sequences. In this work, we propose a hybrid quantum-classical approach for simulating a class of open system dynamics called random-unitary channels. These channels naturally decompose into a series of convex unitary evolutions, which can then be efficiently sampled and run as independent circuits. The method does not require deep ancilla frameworks and thus can be implemented with lower noise costs. We implement simulations of open quantum systems up to dozens of qubits and with large channel ranks. Published by the American Physical Society 2024

Quantum computing for solid mechanics and structural engineering – A demonstration with Variational Quantum Eigensolver

Variational quantum algorithms exploit the features of superposition and entanglement to optimize a cost function efficiently by manipulating the quantum states. They are suitable for noisy intermediate-scale quantum (NISQ) computers that recently became accessible to the worldwide research community. Here, we implement and demonstrate the numerical processes on the 5-qubit and 7-qubit quantum processors on the IBM Qiskit Runtime platform. We combine the commercial finite-element-method (FEM) software ABAQUS with the implementation of Variational Quantum Eigensolver (VQE) to establish an integrated pipeline. Three examples are used to investigate the performance: a hexagonal truss, a Timoshenko beam, and a plane-strain continuum. We conduct parametric studies on the convergence of fundamental natural frequency estimation using this hybrid quantum-classical approach. Our findings can be extended to problems with many more degrees of freedom when quantum computers with hundreds of qubits become available in the near future.

A hybrid quantum-classical approach for inference on restricted Boltzmann machines

A hybrid quantum-classical approach for inference on restricted Boltzmann machines

Coordinated post-disaster restoration for resilient urban distribution systems: A hybrid quantum-classical approach

Incorporating multiple resilient resources into coordinated post-disaster restoration (CPR) strategy contributes positively to resilience enhancement of power distribution systems (PDS). However, the consideration of multiple factors may exacerbate model complexity, resulting in longer solution times and compromising the strategy’s practicality. With the remarkable potential power of quantum computing (QC), we propose a hybrid quantum-classical (HQC) approach for this problem. A HQC-based framework is proposed and the CPR model is established considering repair crew dispatch, PDS operation, microgrids operation, and topology reconfiguration. Then, a hybrid quantum-classical Benders decomposition (HQC-BD) algorithm and detailed pseudocode are proposed and presented in compact form. The integer slack and binary expansion methods are applied to transform the constrained problem into quadratic unconstrained binary optimization problem. Finally, the effectiveness and computational efficiency of the proposed HQC-BD approach are verified. The comparative analysis of different calculation methods is conducted by employing the D-Wave’s direct quantum processing unit solvers and hybrid solvers via the Leap™ quantum cloud service. This paper explores the possibility of quantum-accelerated resilience restoration and enhancement from the HQC point of view.

Well-conditioned multi-product formulas for hardware-friendly Hamiltonian simulation

Simulating the time-evolution of a Hamiltonian is one of the most promising applications of quantum computers. Multi-Product Formulas (MPFs) are well suited to replace standard product formulas since they scale better with respect to time and approximation errors. Hamiltonian simulation with MPFs was first proposed in a fully quantum setting using a linear combination of unitaries. Here, we analyze and demonstrate a hybrid quantum-classical approach to MPFs that classically combines expectation values evaluated with a quantum computer. This has the same approximation bounds as the fully quantum MPFs, but, in contrast, requires no additional qubits, no controlled operations, and is not probabilistic. We show how to design MPFs that do not amplify the hardware and sampling errors, and demonstrate their performance. In particular, we illustrate the potential of our work by theoretically analyzing the benefits when applied to a classically intractable spin-boson model, and by computing the dynamics of the transverse field Ising model using a classical simulator as well as quantum hardware. We observe an error reduction of up to an order of magnitude when compared to a product formula approach by suppressing hardware noise with Pauli Twirling, pulse efficient transpilation, and a novel zero-noise extrapolation based on scaled cross-resonance pulses. The MPF methodology reduces the circuit depth and may therefore represent an important step towards quantum advantage for Hamiltonian simulation on noisy hardware.

Mechanism and Dynamics of Photodecarboxylation Catalyzed by Lactate Monooxygenase.

Photoenzymes are a rare class of biocatalysts that use light to facilitate chemical reactions. Many of these catalysts utilize a flavin cofactor to absorb light, suggesting that other flavoproteins might have latent photochemical functions. Lactate monooxygenase is a flavin-dependent oxidoreductase previously reported to mediate the photodecarboxylation of carboxylates to afford alkylated flavin adducts. While this reaction holds a potential synthetic value, the mechanism and synthetic utility of this process are unknown. Here, we combine femtosecond spectroscopy, site-directed mutagenesis, and a hybrid quantum-classical computational approach to reveal the active site photochemistry and the role the active site amino acid residues play in facilitating this decarboxylation. Light-induced electron transfer from histidine to flavin was revealed, which has not been reported in other proteins. These mechanistic insights enable the development of catalytic oxidative photodecarboxylation of mandelic acid to produce benzaldehyde, a previously unknown reaction for photoenzymes. Our findings suggest that a much wider range of enzymes have the potential for photoenzymatic catalysis than has been realized to date.

Simulating large-size quantum spin chains on cloud-based superconducting quantum computers

Quantum computers have the potential to efficiently simulate large-scale quantum systems for which classical approaches are bound to fail. Even though several existing quantum devices now feature total qubit numbers of more than 100, their applicability remains plagued by the presence of noise and errors. Thus, the degree to which large quantum systems can successfully be simulated on these devices remains unclear. Here, we report on numerical results of physics-motivated variational ansatzes, as well as cloud simulations performed on several of IBM's superconducting quantum computers to simulate ground states of spin chains having a wide range of system sizes up to 102 qubits. Our numerical analysis shows that the accuracy of the ground-state energy and fidelity improves substantially by increasing the number of layers used in the ansatzes. From the cloud experiments, we find that the ground-state energies extracted from realizations across different quantum computers and system sizes reach the expected values to within errors that are small (i.e., on the percent level), including the inference of the energy density in the thermodynamic limit from these values. We achieve this accuracy through a combination of physics-motivated variational ansatzes, and efficient, scalable energy-measurement and error-mitigation protocols, including the use of a reference state in the zero-noise extrapolation. By using a 102-qubit system, we have been able to successfully apply up to 3186 CNOT gates in a single circuit when performing gate-error mitigation. Our accurate, error-mitigated results for random parameters in the ansatz states suggest that a standalone hybrid quantum-classical variational approach for large-scale $XXZ$ models considered in this work is feasible.

Hybrid quantum-classical multi-cut Benders approach with a power system application

Leveraging the current generation of quantum devices to solve optimization problems of practical interest necessitates the development of hybrid quantum-classical (HQC) solution approaches. In this paper, a multi-cut Benders decomposition (BD) approach that exploits multiple feasible solutions of the master problem (MP) to generate multiple valid cuts is adapted, so as to be used as an HQC solver for general mixed-integer linear programming (MILP) problems. The use of different cut selection criteria and strategies to manage the size of the MP by eliciting a subset of cuts to be added in each iteration of the BD scheme using quantum computing is discussed. The HQC optimization algorithm is applied to the Unit Commitment (UC) problem. UC is a prototypical use case of optimization applied to electrical power systems, a critical sector that may benefit from advances in quantum computing. The proposed approach is demonstrated using the D-Wave Advantage 4.1 quantum annealer.

Quantum-Classical Computational Molecular Design of Deuterated High-Efficiency OLED Emitters

This paper describes a hybrid quantum-classical computational approach to designing synthesizable deuterated tris(8-hydroxyquinolinato) aluminum (Alq 3 ) emitters with desirable emission quantum efficiency (QE). This multi-pronged approach first uses classical quantum chemistry to create a machine learning dataset, which is then used to construct an Ising Hamiltonian by a factorization-machine-based model to predict the QEs of Alq 3 emitters. Finally, the Ising Hamiltonian is applied to perform simulations using the variational quantum eigensolver (VQE) and quantum approximate optimization algorithm (QAOA) on a quantum device to discover molecules with optimal QE. Moreover, to improve the simulations on the noisy quantum device, we developed the recursive probabilistic variable elimination method, which recursively eliminates qubits depending on the probability that each qubit has a binary value. We demonstrated that the accuracy of VQE and QAOA optimized for a noisy device can be improved from a probability of 0.075 to 0.97.

Folding lattice proteins with quantum annealing

Quantum annealing is a promising approach for obtaining good approximate solutions to difficult optimization problems. Folding a protein sequence into its minimum-energy structure represents such a problem. For testing new algorithms and technologies for this task, the minimal lattice-based HP model is well suited, as it represents a considerable challenge despite its simplicity. The HP model has favorable interactions between adjacent, not directly bound hydrophobic residues. Here, we develop a novel spin representation for lattice protein folding tailored for quantum annealing. With a distributed encoding onto the lattice, it differs from earlier attempts to fold lattice proteins on quantum annealers, which were based upon chain growth techniques. With our encoding, the Hamiltonian by design has the quadratic structure required for calculations on an Ising-type annealer, without having to introduce any auxiliary spin variables. This property greatly facilitates the study of long chains. The approach is robust to changes in the parameters required to constrain the spin system to chain-like configurations, and performs very well in terms of solution quality. The results are evaluated against existing exact results for HP chains with up to $N=30$ beads with 100% hit rate, thereby also outperforming classical simulated annealing. In addition, the method allows us to recover the lowest known energies for $N=48$ and $N=64$ HP chains, with similar hit rates. These results are obtained by the commonly used hybrid quantum-classical approach. For pure quantum annealing, our method successfully folds an $N=14$ HP chain. The calculations were performed on a D-Wave Advantage quantum annealer.